Scalable neural hardware for the noisy-or model of bayesian networks

ABSTRACT

Embodiments of the invention relate to a scalable neural hardware for the noisy-OR model of Bayesian networks. One embodiment comprises a neural core circuit including a pseudo-random number generator for generating random numbers. The neural core circuit further comprises a plurality of incoming electronic axons, a plurality of neural modules, and a plurality of electronic synapses interconnecting the axons to the neural modules. Each synapse interconnects an axon with a neural module. Each neural module receives incoming spikes from interconnected axons. Each neural module represents a noisy-OR gate. Each neural module spikes probabilistically based on at least one random number generated by the pseudo-random number generator unit.

This invention was made with Government support under HR0011-09-C-0002awarded by Defense Advanced Research Projects Agency (DARPA). TheGovernment has certain rights in this invention.

BACKGROUND

Embodiments of the invention relate to neuromorphic and synaptroniccomputation, and in particular, a scalable neural hardware for thenoisy-OR model of Bayesian networks.

Neuromorphic and synaptronic computation, also referred to as artificialneural networks, are computational systems that permit electronicsystems to essentially function in a manner analogous to that ofbiological brains. Neuromorphic and synaptronic computation do notgenerally utilize the traditional digital model of manipulating 0s and1s. Instead, neuromorphic and synaptronic computation create connectionsbetween processing elements that are roughly functionally equivalent toneurons of a biological brain. Neuromorphic and synaptronic computationmay comprise various electronic circuits that are modeled on biologicalneurons.

In biological systems, the point of contact between an axon of a neuronand a dendrite on another neuron is called a synapse, and with respectto the synapse, the two neurons are respectively called pre-synaptic andpost-synaptic. The essence of our individual experiences is stored inconductance of the synapses. The synaptic conductance changes with timeas a function of the relative spike times of pre-synaptic andpost-synaptic neurons, as per spike-timing dependent plasticity (STDP).The STDP rule increases the conductance of a synapse if itspost-synaptic neuron fires after its pre-synaptic neuron fires, anddecreases the conductance of a synapse if the order of the two firingsis reversed.

BRIEF SUMMARY

Embodiments of the invention relate to a scalable neural hardware forthe noisy-OR model of Bayesian networks. One embodiment comprises aneural core circuit including a pseudo-random number generator forgenerating random numbers. The neural core circuit further comprises aplurality of incoming electronic axons, a plurality of neural modules,and a plurality of electronic synapses interconnecting the axons to theneural modules. Each synapse interconnects an axon with a neural module.Each neural module receives incoming spikes from interconnected axons.Each neural module represents a noisy-OR gate. Each neural module spikesprobabilistically based on at least one random number generated by thepseudo-random number generator.

Another embodiment comprises receiving one or more incoming spikes fromone or more incoming axons in a neural network, and probabilisticallygenerating an outgoing spike in response to said one or more incomingspikes. The outgoing spike is probabilistically generated based on ormore random numbers using a noisy-OR gate model.

These and other features, aspects and advantages of the presentinvention will become understood with reference to the followingdescription, appended claims and accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a neural core circuit, in accordance with an embodiment ofthe invention;

FIG. 2 shows a noisy-OR system including only one noisy-OR neuralmodule, in accordance with an embodiment of the invention;

FIG. 3 shows a noisy-OR system including multiple noisy-OR neuralmodules, in accordance with an embodiment of the invention;

FIG. 4 is a block diagram showing a neuron computation circuit for anoisy-OR neural module, wherein the neuron computation circuit isconfigured to compute an exponential function, in accordance with anembodiment of the invention;

FIG. 5 is a block diagram showing a neuron computation circuit for anoisy-OR neural module, wherein the neuron computation circuit includesa dendrite gate unit, in accordance with an embodiment of the invention;

FIG. 6 shows a scalable noisy-OR neural network, in accordance with anembodiment of the invention;

FIG. 7 is an example graph plotting the spiking probabilities ofdifferent example noisy-OR neural modules, wherein each neural modulehas a different probability r, in accordance with an embodiment of theinvention;

FIG. 8 is an example graph plotting the spiking probabilities ofdifferent example noisy-OR neural modules, wherein each neural modulehas a different spiking threshold V_(th), in accordance with anembodiment of the invention;

FIG. 9 is an example graph plotting the spiking probabilities ofdifferent example noisy-OR neural modules, wherein each neural modulehas a different spiking threshold V_(th) and maintains a differentprobability r, in accordance with an embodiment of the invention;

FIG. 10 is a flowchart of an example process for implementingprobabilistic spiking in a neural module, wherein the process includescomputing an exponential function, in accordance with an embodiment ofthe invention;

FIG. 11 is a flowchart of an example process for implementingprobabilistic spiking in a neural module, wherein the process includesdetermining whether the number of inputs integrated in the neural moduleis greater than a spiking threshold of the neural module, in accordancewith an embodiment of the invention; and

FIG. 12 shows a high level block diagram of an information processingsystem useful for implementing one embodiment of the present invention.

DETAILED DESCRIPTION

Embodiments of the invention relate to a scalable neural hardware forthe noisy-OR model of Bayesian networks. One embodiment comprises aneural core circuit including a pseudo-random number generator forgenerating random numbers. The neural core circuit further comprises aplurality of incoming electronic axons, a plurality of neural modules,and a plurality of electronic synapses interconnecting the axons to theneural modules. Each synapse interconnects an axon with a neural module.Each neural module receives incoming spikes from interconnected axons.Each neural module represents a noisy-OR gate. Each neural module spikesprobabilistically based on at least one random number generated by thepseudo-random number generator.

Another embodiment comprises receiving one or more incoming spikes fromone or more incoming axons in a neural network, and probabilisticallygenerating an outgoing spike in response to said one or more incomingspikes. The outgoing spike is probabilistically generated based on ormore random numbers using a noisy-OR gate model.

In one embodiment, each neural module integrates incoming spikesreceived from interconnected axons, and maintains at least oneconfigurable probability value. Each probability value maintained ineach neural module represents a probability that said neural moduleintegrates an incoming spike. Each neural module computes a spikingprobability, wherein the computed spiking probability represents aprobability that said neural module generates an outgoing spike. Foreach neural module, the computed spiking probability is based on thenumber of integrated spikes and a probability value maintained in saidneural module. Each neural module retrieves a random number from thepseudo-random number generator, and generates an outgoing spike only ifthe retrieved random number is less than the computed spikingprobability.

In another embodiment, each neural module maintains at least oneconfigurable probability value, wherein each probability valuemaintained in said neural module represents a probability that saidneural module integrates an incoming spike. Each neural module receivesincoming spikes from interconnected axons. For each incoming spikereceived, each neural module retrieves a random number from thepseudo-random number generator, and integrates said incoming spike onlyif the retrieved random number is less than a probability valuemaintained in said neural module. Each neural module generates anoutgoing spike only if the number of integrated spikes exceeds aconfigurable spiking threshold of said neural module.

In one embodiment, the neural core circuit is organized into a scalablenoisy-OR neural network including multiple layers of neural corecircuits, wherein outgoing spikes from neural modules of a layer arerouted to incoming axons of a subsequent layer.

The term electronic neuron as used herein represents an architectureconfigured to simulate a biological neuron. An electronic neuron createsconnections between processing elements that are roughly functionallyequivalent to neurons of a biological brain. As such, a neuromorphic andsynaptronic system comprising electronic neurons according toembodiments of the invention may include various electronic circuitsthat are modeled on biological neurons. Further, a neuromorphic andsynaptronic system comprising electronic neurons according toembodiments of the invention may include various processing elements(including computer simulations) that are modeled on biological neurons.Although certain illustrative embodiments of the invention are describedherein using electronic neurons comprising electronic circuits, thepresent invention is not limited to electronic circuits. A neuromorphicand synaptronic system according to embodiments of the invention can beimplemented as a neuromorphic and synaptronic architecture comprisingcircuitry, and additionally as a computer simulation. Indeed,embodiments of the invention can take the form of an entirely hardwareembodiment, an entirely software embodiment, or an embodiment containingboth hardware and software elements.

Embodiments of the invention provide neurons (“neural modules”) thatmodel noisy-OR gates. The noisy-OR neural modules may be used to performBayesian computations, such as performing statistical interference,recognizing patterns, and classifying inputs.

FIG. 1 shows a neural core circuit 100, in accordance with an embodimentof the invention. The neural core circuit 100 comprises multiplepre-synaptic axons 15 and multiple post-synaptic noisy-OR neural modules11. Specifically, the neural core circuit 100 comprises K axons 15 and Mneural modules 11, such as axons A₁, A₂, A₃, . . . , and A_(K), andneural modules N₁, N₂, N₃, . . . , and N_(M), wherein K and M arepositive integers. Each axon 15 and each neural module 11 hasconfigurable operational parameters. Each neural module 11 is connectedto a corresponding dendrite 16, wherein said neural module 11 receivesincoming firing events (e.g., incoming spikes) via its correspondingdendrite 16. As shown in FIG. 1, the neural modules N₁, N₂, N₃, . . . ,and N_(M) have corresponding dendrites D₁, D₂, D₃, . . . , and D_(M),respectively.

As described in detail later herein, each neural module 11 includes aneuron computation circuit that represents a noisy-OR gate. A noisy-ORgate is a canonical interaction model used to describe the interactionbetween multiple n causes X₁, X₂, . . . , X_(n) and their common effectY. Each cause X₁ is assumed to be sufficient to cause Y independent ofthe present of other causes. In one embodiment, each neural module 11shares the same neuron computation circuit (i.e., multiplexed) with itscorresponding dendrite 16.

The neural core circuit 100 further comprises a synaptic crossbar 12including multiple synapses 31, multiple rows/axon paths 26, andmultiple columns/dendrite paths 34. Each synapse 31 communicates firingevents between a pre-synaptic axon 15 and a post-synaptic neural module11. Specifically, each synapse 31 is located at cross-point junctionbetween an axon path 26 and a dendrite path 34, such that a connectionbetween the axon path 26 and the dendrite path 34 is made through saidsynapse 31. Each axon 15 is connected to an axon path 26, such that saidaxon 15 transmits sends firing events to the connected axon path 26. Acorresponding dendrite 16 of each neural module 11 is connected to adendrite path 34, such that said neural module 11 receives firing eventsfrom the connected dendrite path 34.

Further, each axon 15 has a corresponding memory unit 10 maintaining twoor more bits of information designating an axon type (e.g., excitatory,inhibitory) of said axon 15. As shown in FIG. 1, the axons A₁, A₂, A₃, .. . , and A_(K) have corresponding memory units G₁, G₂, G₃, . . . , andG_(K), respectively. The operational parameters of each neural module 11includes a strength parameter for each axon type. Each spike integratedby a neural module 11 is weighted based on a strength parameter for theaxon type of the axon 15 that said spike is received from.

Each synapse 31 has a synaptic weight. The synaptic weights of thesynapses 31 may be represented by a weight matrix W, wherein an elementW_(ij) represents a synaptic weight of a synapse 31 located at row/axonpath i and column/dendrite path j of the crossbar 12. In one embodiment,the synapses 31 are binary memory devices. Each synapse 31 can have aweight “0” indicating that said synapse 31 is non-conducting, or aweight “1” indicating that said synapse 31 is conducting. A learningrule such as spike-timing dependent plasticity (STDP) may be applied toupdate the synaptic weights of the synapses 31.

In this specification, an axon vector 30 is used to represent the axonactivity of every axon 15 of the neural core circuit 100 in a time step.Specifically, each index of the axon vector 30 represents the axonactivity of a corresponding axon 15 of the neural core circuit 100. Eachindex with a bit-value of “1” indicates that a corresponding axon 15 hasreceived a firing event in the current time step, wherein the firingevent received was generated by a neuron in a previous time step. Eachindex with a bit-value of “0” indicates that a corresponding axon 15 hasnot received a firing event in the current time step. For example, asshown in FIG. 1, an axon vector 30 with values <1, 0, 1, . . . , 0>represents that axons A₁ and A₃ have received a firing event in thecurrent time step.

The neural core circuit 100 further comprises an address-event decoder40, an address-event encoder 50, and a lookup table (LUT) 51. Theaddress-event decoder 40 is configured to receive address-event packetsone at a time. Each address-event packet received includes a firingevent generated by a neural module 11 in the same, or a different,neural core circuit 100. Each address-event packet further includesrouting information, such as an address of a target incoming axon 15.The address-event decoder 40 decodes each address-event packet receivedand delivers the firing event in said address-event packet to the targetincoming axon 15. Upon receiving a firing event, each axon 15 activatesthe axon path 26 it is connected to, triggering a read of the axon typeof said axon 15 and all synaptic weights on the axon path 26.

In this specification, an output vector 20 is used to represent theneuron activity of every neural module 11 of the neural core circuit 100in a time step. Specifically, each index of the output vector 20represents the neuron activity of a corresponding neural module 11 ofthe neural core circuit 100. Each index with a bit-value of “1”indicates a firing event generated by a corresponding neural module 11in the current time step, wherein the firing event will be routed to atarget incoming axon 15 in the same, or a different, neural core circuit100. Each index with a bit-value of “0” indicates that a correspondingneural module 11 did not receive sufficient input to generate a firingevent. For example, as shown in FIG. 1, the output vector 20 with values<1, 1, 0, . . . , 1> indicates that neurons N₁, N₂, and N_(M) are active(i.e., generated a firing event) and neuron N₃ is not active in thecurrent time step. Each neuron N₁, N₂, and N_(M) will send anaddress-event packet including the generated firing event to a targetincoming axon 15 in the same, or a different, neural core circuit 100.

The address-event encoder 50 is configured to receive firing eventsgenerated by the neural modules 11. The LUT 51 is an address routingtable configured to determine target incoming axons 15 for firing eventsgenerated by the neural modules 11 of the neural core circuit 100. Atarget incoming axon 15 may be an incoming axon 15 in the same neuralcore circuit 100 or a different neural core circuit 100. The LUT 51maintains information such as target distance, direction, addresses, anddelivery times. The information maintained in the LUT 51 is used tobuild an address-event packet for each firing event received.

The neural core circuit 100 further comprises a pseudo-random numbergenerator (PRNG) 13. The multibit output of the PRNG 13 is thresholdedto generate random numbers that are either 0 or 1 or can be compared toother values to generate binary spike outputs. Each neural module 11 isconnected to the PRNG 13. As described in detail later herein, in eachtime step, each neural module 11 draws a random number from the PRNG 13to implement the probabilistic spiking of said neural module 11. Inanother embodiment, each neural module 11 includes its own PRNG 13.

As shown in FIG. 1, the neural core circuit 100 further comprises acontrol module (“controller”) 46 that is connected to a clock 49. Theclock 49 produces clock signals used by the controller 46 to generatetime-steps. The controller 46 divides each time-step into operationalphases in the neural core circuit 100 for neuron updates, etc.

As described in detail later herein, each neural module 11 includes aneuron computation circuit that represents a noisy-OR gate.

FIG. 2 shows a noisy-OR system 150 including only one noisy-OR neuralmodule 11, in accordance with an embodiment of the invention. The system150 comprises a set of N axons 15, such as axons X₁, X₂, . . . ,X_(N−1), and X_(N). The system 150 further comprises a neural module 11labeled as neural module Y in FIG. 2. Multiple weighted synapticconnections 31 interconnect the axons 15 to the neural module Y, whereineach synaptic connection 31 interconnects an axon 15 to the neuralmodule Y. Each synaptic connection 31 has a synaptic weight.

The neural module Y is configured to function as an N-input noisy-ORgate, wherein the set of N axons 15 represent a set of N inputs. Asshown in FIG. 2, each synaptic connection 31 interconnecting an axonX_(i) to the neural module Y has a corresponding probability valuer_(i). For example, a synaptic connection 31 interconnecting the axon X₁to the neural module Y has a corresponding probability value r₁, and asynaptic connection 31 interconnecting the axon X_(N) to the neuralmodule Y has a corresponding probability value r_(N). For each firingevent received from an axon X_(i) via a synaptic connection 31, theneural module Y integrates said firing event with probability r_(i).

FIG. 3 shows a noisy-OR system 200 including multiple noisy-OR neuralmodules 11, in accordance with an embodiment of the invention. Thesystem 200 comprises a set of N axons 15, such as axons X₁, X₂, . . . ,X_(N−1), and X_(N). The system 200 further comprises a set of M neuralmodules 11, such as neurons Y₁, Y₂, . . . , Y_(M−1), and Y_(M). Multipleweighted synaptic connections 31 interconnect the axons 15 to the neuralmodules 11, wherein each synaptic connection 31 interconnects an axon 15to a neural module 11. Each synaptic connection 31 has a synapticweight. The synaptic weights of the synaptic connections 31 may berepresented by an N×M matrix W, wherein each synaptic connection 31interconnecting an axon X_(i) to a neural module Y_(j) has acorresponding synaptic weight W_(ij).

Each neural module 11 is configured to function as an N-input noisy-ORgate, wherein the set of N axons 15 represent a set of N inputs. Eachsynaptic connection 31 has a corresponding probability. Theprobabilities of the synaptic connections 31 may be represented by anN×M matrix r, wherein each synaptic connection 31 interconnecting anaxon X_(i) to a neural module Y_(j) has a corresponding probabilityvalue r_(ij). For each firing event received from an axon X_(i) via asynaptic connection 31, each neural module Y_(j) integrates said firingevent with probability r_(ij).

As stated above, embodiments of the present invention provide neuralmodules that model noisy-OR gates. In one embodiment, the presentinvention provides a neural module comprising a neuron computationcircuit configured for computing an exponential function. In anotherembodiment, the present invention provides a neural module comprising aneuron computation circuit that includes a dendrite gate.

FIG. 4 is a block diagram showing a neuron computation circuit 400 for aneural module 11, wherein the neuron computation circuit 400 isconfigured to compute an exponential function, in accordance with anembodiment of the invention. In one embodiment, each neural module 11comprises the neuron computation circuit 400. The circuit 400 comprisesan integrator unit (“integrator”) 2, a memory unit 4, an exponentialfunction unit 5, and a spike check unit 6.

In each time step, the integrator 2 of each neural module 11 isconfigured to receive synaptic inputs (i.e., incoming spikes or incomingfiring events) from axons 15 connected to the neural module 11 viasynapses 31. In one embodiment, the synaptic inputs received are binarysignals comprising of spikes and non-spikes. A spike is represented by1, and a non-spike is represented by 0.

The memory unit 4 of each neural module 11 maintains differentprogrammable probability values r. In one embodiment, the memory unit 4maintains different programmable probability values r for different axontypes (i.e., the probability values r are axon specific). For example,let r_(i) denote the probability a neural module 11 integrates asynaptic input received from an axon 15 with axon type i. If an axontype is denoted as 0, 1, 2, or 3 to differentiate connections withdifferent efficacies, each neural module 11 may maintain differentprogrammable probability values r₀,r₁,r₂, and r₃ for the different axontypes 0, 1, 2, and 3, respectively. In another embodiment, the memoryunit 4 maintains different programmable probability values r fordifferent synaptic connections 31 (i.e., the probability values r aresynapse specific) or different dendrites 16 (i.e., the probabilityvalues r are dendrite specific).

The integrator 2 is further configured to integrate each synaptic inputreceived. Specifically, for each input received via a synapse 31, theintegrator 2 integrates said input only if said input is a spike and thesynapse 31 is a conducting synapse. Let n denote the number of inputsintegrated by the integrator 2 in a time step.

In this specification, the probability that a neural module 11 spikes(“spiking probability”) is denoted as P_spk. In each time step, theexponential function unit 5 is configured to compute P_spk only if n isgreater than 0. The exponential function unit 5 may compute P_spk usingthe following example formula: P_spk=1−e^(−(n*r)).

In each time step, the spike check unit 6 is configured to draw/retrievea random number S from the PRNG 13. The spike check unit 6 determines ifthe random number S drawn is less than P_spk. The neural module 11generates and sends out an outgoing spike only if the random number Sdrawn is less than P_spk. n is reset to zero after the neural module 11spikes.

In another embodiment, the circuit 400 may further comprise a leak unitconfigured to apply a probabilistic positive leak rate to n so that theneural module 11 spikes with some probability even if all inputsreceived are 0 values.

Table 1 below provides example pseudo code demonstrating a sequence ofoperations for implementing probabilistic spiking in a j^(th) neuralmodule 11 in conjunction with the neuron computation circuit 400 in FIG.4.

TABLE 1 For i=1:N,  //N is the number of axons in the neural corecircuit    If A_(i)==1 & W_(ij)==1, //the i^(th) axon fired & thesynapse connecting             the i^(th) axon and the j^(th)            //neural module is a conducting synapse        n=n+1;//Increment the number of integrated inputs, n    Endif; Endfor; If n=0,   No spike; Else  //n>0    Compute P_spk = 1−e^(−(n*r)); //P_spk is theprobability                 that the j^(th) neural module spikes    Drawa uniform random number S; //S is between 0 and 1    IfS<P_spk, //Compare S to P_spk        Send out a spike;    //The j^(th)neural module generates a                 spike only if S<P_spk   Endif; Endif;

FIG. 5 is a block diagram showing a neuron computation circuit 450 for anoisy-OR neural module 11, wherein the neuron computation circuit 450includes a dendrite gate unit 14, in accordance with an embodiment ofthe invention. In another embodiment, each neural module 11 comprisesthe neuron computation circuit 450. The circuit 450 comprises thedendrite gate unit (“dendrite gate”) 14, a memory unit 4, an integratorunit (“integrator”) 2, and a threshold check unit 9.

In each time step, the dendrite gate 14 of a neural module 11 isconfigured to receive synaptic inputs (i.e., incoming spikes or incomingfiring events) from axons 15 connected to the neural module 11 viasynapses 31. In one embodiment, the synaptic inputs received are binarysignals comprising of spikes and non-spikes. A spike is represented by1, and a non-spike is represented by 0.

The memory unit 4 of each neural module 11 maintains differentprogrammable probability values r. In one embodiment, the memory unit 4maintains different programmable probability values r for each differentaxon type (i.e., the probability values r are axon specific). In anotherembodiment, the memory unit 4 maintains different programmableprobability values r for different synaptic connections 31 (i.e., theprobability values r are synapse specific). In another embodiment, thememory unit 4 maintains different programmable probability values r fordifferent dendrites 16 (i.e., the probability values r are dendritespecific). Each probability value r maintained denotes the probabilitythat the neural module 11 integrates a synaptic input received.

The dendrite gate 14 includes a comparator component (“comparator”) 14B.For each spike received via a conducting synapse 31, the dendrite gate14 is further configured to draw a random number S from the PRNG 13, usethe comparator 14B to determine whether the random number S drawn isless than a probability value r maintained in the memory unit 14, andtransmit a binary signal to the integrator 2. Specifically, the dendritegate 14 transmits a 1-bit value to the integrator 2 if the random numberS drawn is less than the probability value r. The dendrite gate 14transmits a 0-bit value to the integrator 2 if the random number S drawnreaches or exceeds the probability value r. As such, the integrator 2integrates a spike only if a random number S drawn for the spike is lessthan the probability value r. Let n denote the number of inputsintegrated by the integrator 2 in a time step.

Each neural module 11 has a programmable spiking threshold V_(th),wherein V_(th) is a positive integer. In one embodiment, the spikingthreshold V_(th) of each neural module 11 is set to 1, such that saidneural module 11 generates and sends out an outgoing spike if theintegrator 2 integrates at least one input. Specifically, the thresholdcheck unit 9 of each neural module 11 is configured to determine if n isgreater than zero. If n is zero, the threshold check unit 9 will notgenerate a spike. If n is greater than zero, the threshold check unit 9generates and sends out an outgoing spike.

Table 2 below provides example pseudo code demonstrating a sequence ofoperations for implementing probabilistic spiking in a j^(th) neuralmodule 11 in conjunction with the neuron computation circuit 450 in FIG.5, wherein the spiking threshold V_(th) of the j^(th) neural module 11is set to 1.

TABLE 2 For i=1:N,   //N is the number of axons in the neural corecircuit    If A_(i)==1 & W_(ij)==1, //the i^(th) axon fired & thesynapse connecting             the i^(th) axon and the j^(th)            //neural module is a conducting synapse       Draw a uniformrandom number S; //S is between 0 and 1       If S<r, //Compare S to theprobability r maintained in the       j^(th) neural module         n=n+1; //Increment the number of integrated inputs, n      Endif;    Endif; Endfor; If n<=0,    No spike; Else    Send out aspike;   //The j^(th) neural module generates             a spike onlyif n>0 Endif;

In another embodiment, the spiking threshold V_(th) of each neuralmodule 11 is greater than 1. As such, the threshold check unit 9 of eachneural module 11 is configured to determine whether the number ofintegrated inputs n exceeds the spiking threshold V_(th) of said neuralmodule 11. Specifically, if n is less than or equal to V_(th), thethreshold check unit 9 will not generate a spike. If n exceeds V_(th),the threshold check unit 9 generates and sends out an outgoing spike.

Table 3 below provides example pseudo code demonstrating a sequence ofoperations for implementing probabilistic spiking in a j^(th) neuralmodule 11 in conjunction with the neuron computation circuit 450 in FIG.5, wherein the spiking threshold V_(th) of the j^(th) neural module 11is greater than 1.

TABLE 3 For i=1:N,  //N is the number of axons in the neural corecircuit    If A_(i)==1 & W_(ij)==1, //the i^(th) axon fired & thesynapse connecting             the i^(th) axon and the j^(th)            //neural module is a conducting synapse       Draw a uniformrandom number S; //S is between 0 and 1       If S<r, //Compare S to theprobability r maintained in the       j^(th) neural module         n=n+1; //Increment the number of integrated inputs, n      Endif;    Endif; Endfor; If n<=V_(th,)    //Compare n to thespiking threshold V_(th) of the       j^(th) neural module    No spike;Else    Send out a spike;   //The j^(th) neural module generates a            spike only if n>V_(th) Endif;

In another embodiment, the circuit 450 may further comprise a leak unitconfigured to apply a probabilistic positive leak rate to n so that theneural module 11 spikes with some probability even if all inputsreceived are 0.

FIG. 6 shows a scalable noisy-OR neural network 500, in accordance withan embodiment of the invention. The number of inputs received by aneural module 11 is limited by the size of the crossbar 12 of the neuralcore circuit 100 containing the neural module 11. For example, for aneural core circuit 100 having only 256 incoming axons, the number ofinputs that a neural module 11 of the neural core circuit 100 canreceive is limited to 256.

Each neural module 11 in the network 500 receives more inputs that aneural core circuit 100 containing said neural module 11 is capable ofreceiving. To overcome the size limitations of each individual neuralcore circuit 100, the network 500 may be implemented by organizingmultiple neural core circuits 100 into multiple layers 501 of neuralcore circuits 100. Each layer 501 comprises at least one neural corecircuit 100. Each neural module 11 of a first layer 501 (e.g., FirstLayer) is configured to model a noisy-OR gate, wherein the output (e.g.,spike) generated is based on more than 256 inputs. Each neural module 11of a second layer 501 (e.g., Second Layer) or an intermediate layer 501is configured to model a pure OR gate. The second layer 501 and theintermediate layers 501 (i.e., the subsequent layers 501 after the firstlayer 501) are configured to integrate all input received. Output fromone layer 501 are routed to a subsequent layer 501 using address-eventpackets.

FIG. 7 shows an example graph 600 plotting the spiking probabilities ofdifferent example noisy-OR neural modules 11, wherein each neural module11 has a different probability value r, in accordance with an embodimentof the invention. Each curve 601, 602, 603, and 604 represents a neuralmodule 11 having a spiking threshold V_(th) set to 1. As such, eachneural module 11 represented in the graph 600 generates an outgoingspike if the number of integrated inputs n in said neural module 11 isgreater than zero. Increasing the probability value r of a neural module11 sharpens the slope of the curve representing the neural module 11.

FIG. 8 shows an example graph 650 plotting the spiking probabilities ofdifferent example noisy-OR neural modules 11, wherein each neural module11 has a different spiking threshold V_(th), in accordance with anembodiment of the invention. Each curve 651, 652, 653, and 654represents a neural module 11 having a spiking threshold V_(th) that isgreater than 1. As such, each curve 651, 652, 653, and 654 represents anoisy sigmoid. Sigmoids are utilized in multiple types of neural andBayesian network applications, such as Restricted Boltzmann machines.

Increasing the spiking threshold V_(th) of a neural module 11 shifts thesigmoid representing the neural module 11 further to the right. Forexample, the curve 651 represents a neural module 11 having a spikingthreshold V_(th) that is greater than a different spiking thresholdV_(th) maintained in a neural module 11 that is represented by the curve654.

FIG. 9 shows an example graph 700 plotting the spiking probabilities ofdifferent example noisy-OR neural modules 11, wherein each neural module11 has a different spiking threshold V_(th) and maintains a differentprobability value r, in accordance with an embodiment of the invention.Each curve 701, 702, 703, and 704 represents a noisy sigmoid. Increasingthe probability value r of a neural module 11 sharpens the slope of thesigmoid representing the neural module 11. The curves intersect atreference point 705. The reference point 705 also indicates the half-waypoint of each curve. As such, the half-way point of a curve is preservedas the slope of the curve changes.

FIG. 10 is a flowchart of an example process 800 for implementingprobabilistic spiking in a neural module, wherein the process 800includes computing an exponential function, in accordance with anembodiment of the invention. In process block 801, synaptic inputs(e.g., incoming spikes) are integrated, wherein the number of inputsintegrated is denoted as n. In process block 802, whether n is greaterthan zero is determined. If n is equal to zero, return to process block801. If n is greater than zero, the probability that the neural modulewill spike (“P_spk”) is determined, as shown in process block 803. Inone example implementation, P_spk is determined by computing1−e^(−(n*r)). In process block 804, a random number S is drawn (e.g.,from a pseudo-random number generator). In process block 805, whether Sis less than P_spk is determined. If S is less than P_spk, proceed toprocess block 806 where the neural module generates and sends anoutgoing spike. If S is equal to or greater than P_spk, return toprocess block 801.

FIG. 11 is a flowchart of an example process 900 for implementingprobabilistic spiking in a neural module, wherein the process 900includes determining whether the number of inputs integrated in theneural module is greater than a spiking threshold of the neural module,in accordance with an embodiment of the invention. In process block 901,whether a synaptic input (e.g., a spike) is received is determined. Ifan input is received, a random number S is drawn (e.g., from apseudo-random number generator) as shown in process block 902. If noinput is received, return to process block 901. In process block 903,whether S is less than a probability value r maintained in the neuralmodule is determined. If S is less than r, the neural module integratesthe received input by incrementing n, wherein n represents the number ofintegrated inputs, as shown in process block 904. If S is equal to orgreater than r, the neural module ignores the received input and returnsto process block 901.

In process block 905, whether n is greater than a spiking thresholdV_(th) of the neural module is determined. If n is greater than V_(th),the neural module generates and sends an outgoing spike as shown inprocess block 906. If n is less than or equal to V_(th), return toprocess block 901.

FIG. 12 is a high level block diagram showing an information processingsystem 300 useful for implementing one embodiment of the presentinvention. The computer system includes one or more processors, such asprocessor 302. The processor 302 is connected to a communicationinfrastructure 304 (e.g., a communications bus, cross-over bar, ornetwork).

The computer system can include a display interface 306 that forwardsgraphics, text, and other data from the communication infrastructure 304(or from a frame buffer not shown) for display on a display unit 308.The computer system also includes a main memory 310, preferably randomaccess memory (RAM), and may also include a secondary memory 312. Thesecondary memory 312 may include, for example, a hard disk drive 314and/or a removable storage drive 316, representing, for example, afloppy disk drive, a magnetic tape drive, or an optical disk drive. Theremovable storage drive 316 reads from and/or writes to a removablestorage unit 318 in a manner well known to those having ordinary skillin the art. Removable storage unit 318 represents, for example, a floppydisk, a compact disc, a magnetic tape, or an optical disk, etc. which isread by and written to by removable storage drive 316. As will beappreciated, the removable storage unit 318 includes a computer readablemedium having stored therein computer software and/or data.

In alternative embodiments, the secondary memory 312 may include othersimilar means for allowing computer programs or other instructions to beloaded into the computer system. Such means may include, for example, aremovable storage unit 320 and an interface 322. Examples of such meansmay include a program package and package interface (such as that foundin video game devices), a removable memory chip (such as an EPROM, orPROM) and associated socket, and other removable storage units 320 andinterfaces 322 which allow software and data to be transferred from theremovable storage unit 320 to the computer system.

The computer system may also include a communication interface 324.Communication interface 324 allows software and data to be transferredbetween the computer system and external devices. Examples ofcommunication interface 324 may include a modem, a network interface(such as an Ethernet card), a communication port, or a PCMCIA slot andcard, etc. Software and data transferred via communication interface 324are in the form of signals which may be, for example, electronic,electromagnetic, optical, or other signals capable of being received bycommunication interface 324. These signals are provided to communicationinterface 324 via a communication path (i.e., channel) 326. Thiscommunication path 326 carries signals and may be implemented using wireor cable, fiber optics, a phone line, a cellular phone link, an RF link,and/or other communication channels.

In this document, the terms “computer program medium,” “computer usablemedium,” and “computer readable medium” are used to generally refer tomedia such as main memory 310 and secondary memory 312, removablestorage drive 316, and a hard disk installed in hard disk drive 314.

Computer programs (also called computer control logic) are stored inmain memory 310 and/or secondary memory 312. Computer programs may alsobe received via communication interface 324. Such computer programs,when run, enable the computer system to perform the features of thepresent invention as discussed herein. In particular, the computerprograms, when run, enable the processor 302 to perform the features ofthe computer system. Accordingly, such computer programs representcontrollers of the computer system.

From the above description, it can be seen that the present inventionprovides a system, computer program product, and method for implementingthe embodiments of the invention. The present invention further providesa non-transitory computer-useable storage medium for neuromorphicevent-driven neural computing in a scalable neural network. Thenon-transitory computer-useable storage medium has a computer-readableprogram, wherein the program upon being processed on a computer causesthe computer to implement the steps of the present invention accordingto the embodiments described herein. References in the claims to anelement in the singular is not intended to mean “one and only” unlessexplicitly so stated, but rather “one or more.” All structural andfunctional equivalents to the elements of the above-described exemplaryembodiment that are currently known or later come to be known to thoseof ordinary skill in the art are intended to be encompassed by thepresent claims. No claim element herein is to be construed under theprovisions of 35 U.S.C. section 112, sixth paragraph, unless the elementis expressly recited using the phrase “means for” or “step for.”

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescription of the present invention has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the invention in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the artwithout departing from the scope and spirit of the invention. Theembodiment was chosen and described in order to best explain theprinciples of the invention and the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated.

What is claimed is:
 1. A method comprising: at an electronic neuron of aneural core circuit: receiving an incoming firing event from anelectronic axon connected to the electronic neuron via an electronicsynapse; integrating, via a computation circuit of the electronicneuron, the incoming firing event; maintaining, on a memory device ofthe electronic neuron, a programmable probability value representing aprobability that the electronic neuron spikes; and modeling theelectronic neuron as a noisy-OR gate configured to perform a Bayesiancomputation by probabilistically generating, via the computationcircuit, an outgoing firing event based on a number of incoming firingevents integrated via the computation circuit, a probabilistic leakrate, and the programmable probability value.
 2. The method of claim 1,wherein the integrating comprises: determining whether the electronicsynapse is a conducting synapse; wherein the incoming firing event isintegrated in response to determining the electronic synapse is aconducting synapse.
 3. The method of claim 1, wherein theprobabilistically generating comprises: applying the probabilistic leakrate to the number of incoming firing events integrated, resulting in amodified number of incoming firing events integrated; and determining aspiking probability of the electronic neuron spiking based on anexponential function, the modified number of incoming firing eventsintegrated, and the programmable probability value.
 4. The method ofclaim 3, wherein the probabilistic leak rate is a positive value, andthe electronic neuron spikes with some probability even if theelectronic synapse is a non-conducting synapse.
 5. The method of claim3, wherein the probabilistically generating further comprises: drawing arandom number from a pseudo-random number generator of the electronicneuron; determining whether a condition is satisfied by comparing therandom number against the spiking probability; and generating anoutgoing firing event in response to determining that the condition issatisfied.
 6. The method of claim 5, wherein the condition is satisfiedif the random number is less than the spiking probability.
 7. The methodof claim 1, wherein the Bayesian computation comprises at least one ofstatistical interference, recognizing patterns, and classifying inputs.8. A method comprising: at an electronic neuron of a neural corecircuit: receiving an incoming firing event from an electronic axonconnected to the electronic neuron via an electronic synapse;maintaining, on a memory device of the electronic neuron, a programmableprobability value representing a probability that the electronic neuronintegrates; modeling the electronic neuron as a noisy-OR gate configuredto perform a Bayesian computation by probabilistically integrating, viaa computation circuit of the electronic neuron, the incoming firingevent based on the programmable probability value; and generating, viathe computation circuit, an outgoing firing event based on a number ofincoming firing events integrated via the computation circuit and aprobabilistic leak rate.
 9. The method of claim 8, wherein theprobabilistically integrating comprises: determining whether theelectronic synapse is a conducting synapse; and in response todetermining the electronic synapse is a conducting synapse: drawing arandom number from a pseudo-random number generator of the electronicneuron; determining whether a condition is satisfied by comparing therandom number against the programmable probability value; andintegrating the incoming firing event in response to determining thatthe condition is satisfied.
 10. The method of claim 9, wherein thecondition is satisfied if the random number is less than theprogrammable probability value.
 11. The method of claim 8, wherein thegenerating comprises: applying the probabilistic leak rate to the numberof incoming firing events integrated, resulting in a modified number ofincoming firing events integrated; determining whether a condition issatisfied by comparing the modified number of incoming firing eventsintegrated against a spiking threshold; and generating an outgoingfiring event in response to determining that the condition is satisfied.12. The method of claim 11, wherein the condition is satisfied if themodified number of incoming firing events integrated exceeds the spikingthreshold.
 13. The method of claim 11, wherein the probabilistic leakrate is a positive value, and the electronic neuron spikes with someprobability even if the electronic synapse is a non-conducting synapse.14. The method of claim 8, wherein the Bayesian computation comprises atleast one of statistical interference, recognizing patterns, andclassifying inputs.